The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation

• 成果类型: Article
• 署名作者: Oates, Chris J.; Papamarkou, Theodore; Girolami, Mark
• 署名单位: University of Technology Sydney
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1021006
• 发表日期: 2016
• 页码: 634-645
• 关键词: chain monte-carlo; marginal likelihood; computation; inference; distributions; algorithms; simulation; scheme; mcmc

摘要

Approximation of the model evidence is well known to be challenging. One promising approach is based on thermodynamic integration, but a key concern is that the thermodynamic integral can suffer from high variability in many applications. This article considers the reduction of variance that can be achieved by exploiting control variates in this setting. Our methodology applies whenever the gradient of both the log likelihood and the log-prior with respect to the parameters can be efficiently evaluated. Results obtained on regression models and popular benchmark datasets demonstrate a significant and sometimes dramatic reduction in estimator variance and provide insight into the wider applicability of control variates to evidence estimation. Supplementary materials for this article are available online.